(REF ) is of the form (3.3) of [1]}, and describes the near-horizon
geometry of extremal rotating black holesMetrics of the type (REF ) were discussed
for the first time in [2]} in the context of the extremal Kerr throat geometry.,
with isometry group \(\text{SL}(2,\hbox{R})\times \text{U}(1)\) .
From (REF ) it is clear that the scalar fields have
a nontrivial dependence on the horizon coordinate \(\xi \)  unless \(g_I{\cal D}_{\alpha }X^I=0\) .
As was shown in [3]}, the solution with constant scalars is the near-horizon
limit of the supersymmetric rotating hyperbolic black holes in minimal gauged
supergravity [4]}.
